Dynamical effects in electron transfer reactions. II. Numerical solution

Current state of the primary charge separation mechanism in photosystem I of cyanobacteria

This review analyzes new data on the mechanism of ultrafast reactions of primary charge separation in photosystem I (PS I) of cyanobacteria obtained in the last decade by methods of femtosecond absorption spectroscopy. Cyanobacterial PS I from many species harbours 96 chlorophyll a (Chl a) molecules, including six specialized Chls denoted Chl1A/Chl1B (dimer P700, or PAPB), Chl2A/Chl2B, and Chl3A/Chl3B arranged in two branches, which participate in electron transfer reactions. The current data indicate that the primary charge separation occurs in a symmetric exciplex, where the special pair P700 is electronically coupled to the symmetrically located monomers Chl2A and Chl2B, which can be considered together as a symmetric exciplex Chl2APAPBChl2B with the mixed excited (Chl2APAPBChl2B)* and two charge-transfer states P700 +Chl2A - and P700 +Chl2B -. The redistribution of electrons between the branches in favor of the A-branch occurs after reduction of the Chl2A and Chl2B monomers. The formation of charge-transfer states and the symmetry breaking mechanisms were clarified by measuring the electrochromic Stark shift of β-carotene and the absorption dynamics of PS I complexes with the genetically altered Chl 2B or Chl 2A monomers. The review gives a brief description of the main methods for analyzing data obtained using femtosecond absorption spectroscopy. The energy levels of excited and charge-transfer intermediates arising in the cyanobacterial PS I are critically analyzed.

Control of electron transfer by protein dynamics in photosynthetic reaction centers

Trehalose and glycerol are low molecular mass sugars/polyols that have found widespread use in the protection of native protein states, in both short- and long-term storage of biological materials, and as a means of understanding protein dynamics. These myriad uses are often attributed to their ability to form an amorphous glassy matrix. In glycerol, the glass is formed only at cryogenic temperatures, while in trehalose, the glass is formed at room temperature, but only upon dehydration of the sample. While much work has been carried out to elucidate a mechanistic view of how each of these matrices interact with proteins to provide stability, rarely have the effects of these two independent systems been directly compared to each other. This review aims to compile decades of research on how different glassy matrices affect two types of photosynthetic proteins: (i) the Type II bacterial reaction center from Rhodobacter sphaeroides and (ii) the Type I Photosystem I reaction center from cyanobacteria. By comparing aggregate data on electron transfer, protein structure, and protein dynamics, it appears that the effects of these two distinct matrices are remarkably similar. Both seem to cause a "tightening" of the solvation shell when in a glassy state, resulting in severely restricted conformational mobility of the protein and associated water molecules. Thus, trehalose appears to be able to mimic, at room temperature, nearly all of the effects on protein dynamics observed in low temperature glycerol glasses.

Tracing the Full Bimolecular Photocycle of Iron(III)-Carbene Light Harvesters in Electron-Donating Solvents

Photoinduced bimolecular charge transfer processes involving the iron(III) N-heterocyclic carbene (FeNHC) photosensitizer [Fe(phtmeimb)₂]⁺ (phtmeimb = phenyltris(3-methyl-imidazolin-2-ylidene)borate) and triethylamine as well as N,N-dimethylaniline donors have been studied using optical spectroscopy. The full photocycle of charge separation and recombination down to ultrashort time scales was studied by investigating the excited-state dynamics up to high quencher concentrations. The unconventional doublet ligand-to-metal charge transfer (²LMCT) photoactive excited state exhibits donor-dependent charge separation rates of up to 1.25 ps^–1 that exceed the rates found for typical ruthenium-based systems and are instead more similar to results reported for organic sensitizers. The ultrafast charge transfer probed at high electron donor concentrations outpaces the solvent dynamics and goes beyond the classical Marcus electron transfer regime. Poor photoproduct yields are explained by donor-independent, fast charge recombination with rates of ∼0.2 ps^–1, thus inhibiting cage escape and photoproduct formation. This study thus shows that the ultimate bottlenecks for bimolecular photoredox processes involving these FeNHC photosensitizers can only be determined from the ultrafast dynamics of the full photocycle, which is of particular importance when the bimolecular charge transfer processes are not limited by the intrinsic excited-state lifetime of the photosensitizer.

First observation of ultrafast intramolecular proton transfer rate between electronic ground states in solution

Despite the importance of ultrafast (time scale exceeding 10(-11) s) intramolecular proton transfer (PT) events between electronic ground states in solution, experimental determination of the rates of such reactions has not yet been accomplished because of the limitations of the utilized methods. The objective of this study was to evaluate the PT rates of intramolecular O···H···O hydrogen-bonded systems in solution through the (1)H spin-lattice relaxation times of the hydroxyl protons, induced by the (1)H-(17)O dipolar interactions (T(1dd)(OH)), taking into account the contribution of the OH reorientational motion to T(1dd)(OH). Solutions of the benzoic acid dimer (BA dimer), 1-benzoyl-6-hydroxy-6-phenylfulvene (Fulvene), and dibenzoylmethane (DBM) were chosen as test systems. For Fulvene in CCl(4), the PT time, τ(PT), was deduced to be 7 × 10(-11) s. In the case of the BA dimer in CCl(4), the τ(PT) value was considerably greater than the OH reorientational correlation time, τ(R(OH)) = 4.3 × 10(-11) s. In contrast, the experimental results for DBM in CCl(4) indicated that the proton is located about midway between the two oxygen atoms, that is, the PT potential energy surface is a single well or a double well with a PT barrier near or below the zero-point energy.

ELECTRON TRANSFER REACTIONS COUPLED TO PROTON TRANSLOCATION: CYTOCHROME OXIDASE, PROTON PUMPS, AND BIOLOGICAL ENERGY TRANSDUCTION

Cytochrome oxidase (COX) is the terminal component of electron transport chain of the respiratory system in mitochondria, and one of the key enzymes responsible for energy generation in cells. COX functions as a proton pump that utilizes free energy of oxygen reduction for translocation of protons across the mitochondrion membrane. The proton gradient created in the process is later utilized to drive synthesis of ATP. Although the structure of COX has been recently resolved, the molecular mechanism of proton pumping remains unknown. In this paper, general principles and possible molecular mechanisms of energy transformations in this enzyme will be discussed. The main question is how exactly chemical energy of oxygen reduction and water formation is transformed into a proton gradient; or, how exactly electron transfer reactions are utilized to translocate protons across the mitochondrion membrane against the electrochemical gradient. A key to the solution of this problem is in understanding correlated transport of electrons and protons. Here, theoretical models are discussed for coupled electron and proton transfer reactions in which an electron is tunneling over long distance between two redox cofactors, and a coupled proton is moving along a proton conducting channel in a classical, diffusion-like random walk fashion. Such reactions are typical for COX and other enzymes involved in biological energy transformations.

Nonequilibrium solvent effects in reaction kinetics — Steady-state solutions for the Agmon–Hopfield two-dimensional stochastic model

We propose an approximate localized-sink approach to the solution of the Agmon–Hopfield two-dimensional stochastic model for reactions in viscous media. The approach yields simple expressions for the sink location and the reaction rate constant, easy to use in the analysis of experimental data, and allows an intuitive phenomenological interpretation of the overall process in terms of a two-step kinetic scheme.

Theory of reversible electron transfer reactions in a condensed phase

We have derived an exact analytical expression for the average forward rate of a reversible electron transfer reaction, modeled through a reaction coordinate undergoing diffusive motion in arbitrary potential wells of the reactant and the product in presence of a localized sink of arbitrary location and strength. The dynamics of diffusive motion is described by employing two coupled generalized diffusion reaction (Smoluchowski) equations with coordinate dependent diffusivity and delta sink. The average forward electron transfer rate constant obtained here for the system, with equilibrium or nonequilibrium distributions as initial condition, is determined by the forward and backward rate constants calculated based on the transition state theory and the weighted average rate for the well dynamics. We also discuss various limiting cases for the rate of electron transfer reactions corresponding to the different experimental situations. As an illustrative example, we have considered back electron transfer (ET) reaction and shown that the present theory can explain the non-Marcus free energy gap dependence of the rate of ET reactions. More importantly, the approach presented here can easily be extended to systems describing the dynamics of diffusive motion in coupled multipotential surfaces associated with electron transfer reactions.

Dynamic solvent effects on the thermal isomerization of zinc dithizonate

The pressure dependence of the rate constant for the thermal isomerization of zinc dithizonate was measured at various temperatures in highly viscous solvents, i.e., glycerol triacetate and 2,4-dicyclohexyl-2-methylpentane, as well as in their chemically similar nonviscous solvents, such as methyl acetate and methylcyclohexane. In the nonviscous solvents, the reaction was slightly retarded upon external pressure suggesting the validity of the transition state theory. On the other hand, in the viscous solvents, the reaction, even at ambient pressure, was strongly retarded by an increase in external pressure suggesting the slow thermal fluctuation of the solvent molecules upon external pressure in highly viscous systems. This made it possible to observe the dynamic solvent effects on the isomerization of zinc dithizonate in viscous solvents. The viscosity dependence of the rate constants was rationalized by the two-dimensional reaction coordinate model.

Molecular dynamics simulations of porphyrin-dendrimer systems: toward modeling electron transfer in solution

We have performed computational simulations of porphyrin-dendrimer systems--a cationic porphyrin electrostatically associated to a negatively charged dendrimer--using the method of classical molecular dynamics (MD) with an atomistic force field. Previous experimental studies have shown a strong quenching effect of the porphyrin fluorescence that was assigned to electron transfer (ET) from the dendrimer's tertiary amines (Paulo, P. M. R.; Costa, S. M. B. J. Phys. Chem. B 2005, 109, 13928). In the present contribution, we evaluate computationally the role of the porphyrin-dendrimer conformation in the development of a statistical distribution of ET rates through its dependence on the donor-acceptor distance. We started from simulations without explicit solvent to obtain trajectories of the donor-acceptor distance and the respective time-averaged distributions for two dendrimer sizes and different initial configurations of the porphyrin-dendrimer pair. By introducing explicit solvent (water) in our simulations, we were able to estimate the reorganization energy of the medium for the systems with the dendrimer of smaller size. The values obtained are in the range 0.6-1.5 eV and show a linear dependence with the inverse of the donor-acceptor distance, which can be explained by a two-phase dielectric continuum model taking into account the medium heterogeneity provided by the dendrimer organic core. Dielectric relaxation accompanying ET was evaluated from the simulations with explicit solvent showing fast decay times of some tens of femtoseconds and slow decay times in the range of hundreds of femtoseconds to a few picoseconds. The variations of the slow relaxation times reflect the heterogeneity of the dendrimer donor sites which add to the complexity of ET kinetics as inferred from the experimental fluorescence decays.

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Protein dynamics control of electron transfer in photosynthetic reaction centers from Rps. sulfoviridis

In the cycle of photosynthetic reaction centers, the initially oxidized special pair of bacteriochlorophyll molecules is subsequently reduced by an electron transferred over a chain of four hemes of the complex. Here, we examine the kinetics of electron transfer between the proximal heme c-559 of the chain and the oxidized special pair in the reaction center from Rps. sulfoviridis in the range of temperatures from 294 to 40 K. The experimental data were obtained for three redox states of the reaction center, in which one, two, or three nearest hemes of the chain are reduced prior to special pair oxidation. The experimental kinetic data are analyzed in terms of a Sumi-Marcus-type model developed in our previous paper,1 in which similar measurements were reported on the reaction centers from Rps. viridis. The model allows us to establish a connection between the observed nonexponential electron-transfer kinetics and the local structural relaxation dynamics of the reaction center protein on the microsecond time scale. The activation energy for relaxation dynamics of the protein medium has been found to be around 0.1 eV for all three redox states, which is in contrast to a value around 0.4-0.6 eV in Rps. viridis.1 The possible nature of the difference between the reaction centers from Rps. viridis and Rps. sulfoviridis, which are believed to be very similar, is discussed. The role of the protein glass transition at low temperatures and that of internal water molecules in the process are analyzed.

Hot recombination of photogenerated ion pairs

The recombination dynamics of ion pairs generated upon electron transfer quenching of perylene in the first singlet excited state by tetracyanoethylene in acetonitrile is quantitatively described by the extended unified theory of photoionization/recombination. The extension incorporates the hot recombination of the ion pair passing through the level-crossing point during its diffusive motion along the reaction coordinate down to the equilibrium state. The ultrafast hot recombination vastly reduces the yield of equilibrated ion pairs subjected to subsequent thermal charge recombination and separation into free ions. The relatively successful fit of the theory to the experimentally measured kinetics of ion accumulation/recombination and free ion yield represents a firm justification of hot recombination of about 90% of primary generated ion pairs.

Dynamic effects of nonequilibrium solvation: Potential and free energy surfaces for Z/E isomerization in solvent-solute coordinates

A novel definition of a solvent coordinate associated with a given reaction is formulated in terms of molecular-dynamic trajectories of the solvent and is applied to discuss the topography of potential energy and free energy surfaces of model liquid phase Z/E isomerization reactions in solvent-solute coordinates. It is shown that the arrangement of the reactant and product valleys on these surfaces can vary from consecutive to parallel, depending on the strength of the solvent-solute interactions.

Quantum effect of intramolecular high-frequency vibrational modes on diffusion-controlled electron transfer rate: From the weak to the strong electronic coupling regions

The Sumi-Marcus theory is extended by introducing two approaches to investigate electron transfer reactions from weak-to-strong electronic coupling regime. One of these approaches is the quantum R-matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reaction-diffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Landau-Zener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.